Analysis of anomalous quartic $WWZ\gamma$ couplings in $\gamma p$ collision at the LHC

Gauge boson self-couplings are exactly determined by the non-Abelian gauge nature of the Standard Model (SM), thus precision measurements of these couplings at the LHC provide an important opportunity to test the gauge structure of the SM and the spontaneous symmetry breaking mechanism. It is a common way to examine the physics of anomalous quartic gauge boson couplings via effective Lagrangian method. In this work, we investigate the potential of the process $pp\rightarrow p\gamma p\rightarrow p W Z q X$ to analyze anomalous quartic $WWZ\gamma$ couplings by two different CP-violating and CP-conserving effective Lagrangians at the LHC. We calculate $95\%$ confidence level limits on the anomalous coupling parameters with various values of the integrated luminosity. Our numerical results show that the best limits obtained on the anomalous couplings $\frac{k_{0}^{W}}{\Lambda^{2}}$, $\frac{k_{c}^{W}}{\Lambda^{2}}$, $\frac{k_{2}^{m}}{\Lambda^{2}}$ and $\frac{a_{n}}{\Lambda^{2}}$ at $\sqrt{s}=14$ TeV and an integrated luminosity of $L_{int}=100$ fb$^{-1}$ are $[-1.37;\, 1.37]\times 10^{-6}$ GeV$^{-2}$, $[-1.88; \, 1.88]\times 10^{-6}$ GeV$^{-2}$, $[-6.55; \, 6.55]\times 10^{-7}$ GeV$^{-2}$ and $[-2.21;\,2.21]\times 10^{-6}$ GeV$^{-2}$, respectively. Thus, $\gamma p$ mode of photon-induced reactions at the LHC highly improves the sensitivity limits of the anomalous coupling parameters $\frac{k_{0}^{W}}{\Lambda^{2}}$, $\frac{k_{c}^{W}}{\Lambda^{2}}$, $\frac{k_{2}^{m}}{\Lambda^{2}}$ and $\frac{a_{n}}{\Lambda^{2}}$.